[Submitted on 29 Jul 2026]

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Abstract:Jacobs comprehension categories subsume a large class of categorical models of type dependency, supporting also the description of morphisms between types. We study the relationship between comprehension categories and a particular subclass, which we call Lawvere-Ehrhard comprehension categories. First, we characterize this subclass by comparing a fibration of terms and a fibration of type morphisms associated to a given comprehension category. Next, we provide the construction of the free comprehension category over a fibration. Finally, we construct the free Lawvere-Ehrhard comprehension category over a Jacobs comprehension category.

Submission history

From: Andrea Giusto [view email]
[v1] Wed, 29 Jul 2026 17:45:10 UTC (58 KB)